No, the property you describe is called "preimage resistance". Collision resistance is stronger; it states that an attacker should not be able to create a pair of inputs with the same hash. In the case of md5, creating a pair of inputs with the same hash is easier than creating another input with the same hash as something else which you didn't yourself generate.

The MD5 algorithm is known to lack collision resistance, but whether it has preimage resistance is less certain; mathematical advances have weakened its preimage resistance, but not yet to the point of demonstrating a practical preimage attack.